A tool of this kind is described e.g. in the U.S. Pat. No. 4,130,031 of the inventors. The housing of this known tool is defined by a first jaw means in which a support for the treated conductor, defined by a V-spaped recess into which one or more knife blades of a cutting means project is provided intermediate the two ends of the jaw means. At one said end is to the first jaw means pivoted a second jaw means defining a pushing means by which an inserted conductor can be pressed against the cutting means. At the other said end is a means for locking both jaws means in their closed position provided, viz. a protruding finger which can hold the second jaw means and which is integrated with a gripping means defined by an eye through which the user can put his finger in order to twirl the tool about the inserted conductor, and so to extend the only local incision or incisions along the entire cross-sectional periphery of the conductor. However, the said manner of forcing the cutting means into the insulation and of locking the two jaw means may sometimes be difficult to carry out, particularly with hard and/or encrusted insulation layers.